Orthogonal polynomials, Jacobi matrices and random matrices

2008 ◽  
pp. 249-263
Author(s):  
L. Pastur
Keyword(s):  
Orthogonal Polynomials ◽  
Random Matrices ◽  
Jacobi Matrices

scholarly journals Self-adjoint Jacobi matrices on trees and multiple orthogonal polynomials

2019 ◽  
Vol 373 (2) ◽  
pp. 875-917 ◽  
Author(s):  
Alexander I. Aptekarev ◽  
Sergey A. Denisov ◽  
Maxim L. Yattselev
Keyword(s):  
Orthogonal Polynomials ◽  
Jacobi Matrices ◽  
Multiple Orthogonal Polynomials

Continuity of the Lyapunov exponent for analytic quasiperiodic cocycles

2009 ◽  
Vol 29 (6) ◽  
pp. 1881-1905 ◽  
Author(s):  
S. JITOMIRSKAYA ◽  
D. A. KOSLOVER ◽  
M. S. SCHULTEIS
Keyword(s):  
Lyapunov Exponent ◽  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Quantum Dynamics ◽  
Jacobi Matrices

AbstractIt is known that the Lyapunov exponent is not continuous at certain points in the space of continuous quasiperiodic cocycles. In this paper we show that it is continuous in the analytic category. Our corollaries include continuity of the Lyapunov exponent associated with general quasiperiodic Jacobi matrices or orthogonal polynomials on the unit circle, in various parameters, and applications to the study of quantum dynamics.

scholarly journals Persymmetric Jacobi matrices, isospectral deformations and orthogonal polynomials

2017 ◽  
Vol 450 (2) ◽  
pp. 915-928 ◽  
Author(s):  
Vincent X. Genest ◽  
Satoshi Tsujimoto ◽  
Luc Vinet ◽  
Alexei Zhedanov
Keyword(s):  
Orthogonal Polynomials ◽  
Jacobi Matrices
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